\(\left\{\begin{matrix}\left(x+1\right)\left(y+1\right)=8\\x\left(x+1\right)+y\left(y+1\right)+xy=17\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}x+y+xy=7\\x^2+y^2+x+y+xy=17\end{matrix}\right.\)
Đặt \(\left\{\begin{matrix}xy=P\\x+y=S\end{matrix}\right.\) thì
\(\Rightarrow\left\{\begin{matrix}S+P=7\\S^2+S-P=17\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}P=7-S\\S^2+S-\left(7-S\right)=17\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}P=7-S\\S^2+2S=24\end{matrix}\right.\)
\(\Leftrightarrow\left[\begin{matrix}\left\{\begin{matrix}S=-6\\P=13\end{matrix}\right.\\\left\{\begin{matrix}S=4\\P=3\end{matrix}\right.\end{matrix}\right.\)
Giờ chỉ cần thế ngược lại là tìm được x, y